Stability in blocks - static equilibrium

[taq]

Hii,

First of all, I'm from Brazil and my english is not so good!

I've been studied the follwing problem for some months and until today I'm not find a solution!
Please help me.
I have some blocks (2D) stacked like in the figure below (attachment).
In each block I have ONLY the weight force that act on the center of mass.
My problem is:
How I calculte the equilibrium of the system? It is in equilibrium?
And, How much of each force is transferred for the adjacent block and so on until the last block (in contact with the ground)?

I've tried static equilibrium (sum of momentum, sum of forces): But for one block that has three adjacent blocks the system is undetermined, and I need of more equations...
I've also tried three momentum's equations, some techniques of pillar scaling, but... :(

Please help me!

 

[eljose79]

Hello,

Thank you for reaching out for help with your problem. It sounds like you have been working hard to find a solution for some time now. I will do my best to assist you.

First, let's clarify what we mean by equilibrium in this situation. Equilibrium means that the forces acting on the system are balanced and there is no net force or torque acting on the system. This means that the system is not accelerating and is either at rest or moving at a constant velocity.

To determine if your system is in equilibrium, you can use the equations of static equilibrium, which include the sum of forces and the sum of moments. The sum of forces should equal zero, and the sum of moments should also equal zero. If these conditions are met, then the system is in equilibrium.

In your case, it sounds like you have multiple blocks stacked on top of each other, with each block having a weight force acting on its center of mass. To calculate the equilibrium of the system, you will need to consider the forces acting on each individual block as well as the forces acting on the entire system.

To start, you can consider the forces acting on the bottom block, which is in contact with the ground. The weight force of this block will be transferred to the ground, and the ground will exert an equal and opposite normal force on the block. This normal force will then be transferred to the next block above it, and so on.

To determine the forces acting on each block, you can use the principle of action and reaction. This means that for every force acting on a block, there is an equal and opposite force acting on the adjacent block. By considering all of these forces, you can then use the equations of static equilibrium to determine if the system is in equilibrium.

I understand that this may still seem complicated, so I would recommend seeking the help of a physics or engineering tutor who can work through the problem with you step by step. They can also provide additional resources and practice problems to help you better understand the concept of equilibrium.

I hope this helps and good luck with your studies!

 

[charng]

Hi there,

Stability in blocks and static equilibrium is a complex problem, and it's great that you've been studying it for some time now. It's important to remember that in order for a system to be in static equilibrium, the sum of all forces acting on it must be equal to zero and the sum of all moments must also be equal to zero.

In your case, since the only force acting on each block is the weight force, you can calculate the equilibrium of the system by first finding the sum of all weight forces acting on the blocks. This will give you the total weight of the entire system. Then, using this weight, you can calculate the normal force acting on the bottom block from the ground, which will be equal to the weight of the entire system.

Next, you can use the principle of moments to calculate the distribution of forces between the blocks. This will depend on the position of the center of mass for each block and the distance between the blocks. From there, you can determine if the system is in equilibrium or not.

It's important to remember that in a system like this, the forces will be transferred between blocks based on the principle of moments and the position of the center of mass. It may be helpful to draw a free-body diagram for each block and consider the forces acting on it individually.

I hope this helps and good luck with your studies!